$\frac{\cos^2 heta}{\sin^2 heta} - \frac{1}{\sin^2 heta}$, in simplified form, is :

Question

$\frac{\cos^2	heta}{\sin^2	heta} - \frac{1}{\sin^2	heta}$, in simplified form, is :

Accepted Answer

## Model Answer $$\frac{\cos^2	heta}{\sin^2	heta} - \frac{1}{\sin^2	heta} = \frac{\cos^2	heta - 1}{\sin^2	heta} = \frac{-(1-\cos^2	heta)}{\sin^2	heta} = \frac{-\sin^2	heta}{\sin^2	heta} = -1$$ **Answer: (D) −1** ## Explanation Use the identity $\sin^2	heta + \cos^2	heta = 1$, so $\cos^2	heta - 1 = -\sin^2	heta$. The expression simplifies neatly to −1. Source: Ch. 8, Section 8.4 Trigonometric Identities.

Mathematics — Standard (041) — CBSE Class 10 board question